I am stuck at a very basic probability question.
The problem statement -
If a fair coin is flipped twice what is the probability that heads will appear in either the first flip or the second flip?
This is my take on this problem.
If a coin is tossed twice below will be the different combinations that are likely to happen-
So there are 4 possible combinations.SO the probability that heads will appear either in first or in second flip will be 2/4 = 1/2.
However if I try to solve the problem with the help of OR probability I am getting a different answer.
P(A or B) = P(A) + P(B) - P(A and B)
The probability that heads will appear in the first flip is 1/2.The probability that heads will appear in the seocnd flip is 1/2.and the probability that heads will appear in both flips is 1/2*1/2 = 1/4.
Therefore P(H1 or H2) =P(H1) + P(H2) - P(H1 and H2) = 1/2 + 1/2 - 1/4 = 3/4.
Can someone tell me why is there a difference in answer.Am I missing something here?
"what is the probability that heads will appear in either the first flip or the second flip"
means what is the probability that heads will appear in first of second or BOTH flips.
Hence 3 of the four cases - TH,HT,HH - satisfy our condition.
Another way to go about it is 1 - P(Both will be tails) = 1 - 1/4 = 3/4
Formally, 'either A or B' means it must be at least one of A and B. It can be both too.
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